Use the image to answer the question.
An illustration of a coordinate plane with four quadrants shows the x-axis ranging from negative 9 to 9 and the y-axis ranging from negative 11 to 11 in increments of 1. A solid downward line with arrows at both ends is plotted on the graph. The line passes through the plotted points left parenthesis 0 comma 1 right parenthesis and left parenthesis 1 comma negative 4 right parenthesis.
Write the equation of the line in slope-intercept form.
(1 point)
Responses
y=−5x−1
y equals negative 5 x minus 1
y=5x+1
y equals 5 x plus 1
y=−5x+1
y equals negative 5 x plus 1
−5x−y=−1
negative 5 x minus y equals negative 1
To find the equation of the line in slope-intercept form, we first need to find the slope of the line. The slope can be found by using the formula:
slope = (change in y) / (change in x)
Given the points (0,1) and (1,-4), the change in y is -4 - 1 = -5 and the change in x is 1 - 0 = 1.
So, the slope of the line is -5/1, which simplifies to -5.
Next, we can use the point-slope form of the equation of a line:
y - y1 = m(x - x1)
Using the point (1, -4), we have:
y - (-4) = -5(x - 1)
Simplifying further:
y + 4 = -5x + 5
Lastly, we can write the equation in slope-intercept form by isolating y:
y = -5x + 1
Therefore, the correct answer is:
y = -5x + 1.